UPTEC F11 056

Examensarbete 30 hpOktober 2011

IR optical properties in thin films of diamond

Anna Petersson

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

IR optical properties in thin films of diamond

Anna Petersson

In the past decades new interest in diamond and possible applications of diamond hasemerged. In this master thesis, optical properties of thin films of diamond wereinvestigated for the possible use as an Internal Reflection Element (IRE) in AttenuatedTotal Reflection Fourier Infra Red (ATR-FTIR) spectroscopy. First a theoretical studyof optical properties was made using Fresnel’s equations. Secondly the ray-tracingsoftware TracePro was tested as a possible tool for further investigations of opticalproperties in advanced geometries. Finally, experimental measurements were made tocompare the simulated result with measured data. Results obtained with TraceProwere consistent with the theoretically expected results as to dependence of layerthickness, polarization and wavelength, and TracePro was therefore a possible toolfor the investigation of optical properties in thin films. Although no extra informationwas given from TracePro for this specific geometry, TracePro can be a valuable toolin the investigation of more advanced geometries. The experimental measurementsshowed the importance of a well-defined layer thickness and also showed a strongerdependence of the underlying coating materials than expected from simulations.Further investigations need to be made to fully understand the dependence of theunderlying coating materials SiO2 and Si3N4, particularly regarding differentpolarization states.

ISSN: 1401-5757, UPTEC F11 056Examinator: Tomas NybergÄmnesgranskare: Lars ÖsterlundHandledare: Lars Österlund

Sammanfattning

De senaste årtiondena har nytt intresse väckts för diamant och möjliga tillämp-ningar av diamant. I detta examensarbete har optiska egenskaper i tunna �lmerav diamant undersökts för ett möjligt användningsområde som Internal Re�ec-tion Element (IRE) inom Attenuated Total Re�ection Fourier Infra Red (ATR-FTIR) spektroskopi. Först gjordes en teoretisk studie av optiska egenskapermed hjälp av Fresnels ekvationer. I andra steget testades mjukvaran TraceProsom ett möjligt verktyg för vidare studier av optiska egenskaper i tunna �lmermed avancerad geometri. Sist gjordes experimentella mätningar för att jämföradet simulerade resultatet med experimentell data. Resultaten som framtogs medTracePro gav ett resultat samstämmigt med teori med avseende på beroendeav �lmtjocklek, polarisation och våglängd, och TracePro kan därför ses somett möjligt verktyg för att undersöka optiska egenskaper i tunna �lmer. Ävenom ingen ny information erhölls med TracePro för denna speci�ka geometri, kanTracePro bli ett värdefullt verktyg för analys av mer avancerad geometri. De ex-perimentella mätningarna visade på vikten av en välde�nierad �lmtjocklek ochdessutom på ett starkare beroende av underliggande skikt än väntat från simu-leringarna. Vidare analys krävs för att helt förstå beroendet av de underliggandeskikten SiO2 och Si3N4, särskilt med avseende på olika polarisationstillstånd.

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Contents

1 Introduction 51.1 Diamond in bio- and microelectronic applications . . . . . . . . . 51.2 Applications in ATR-FTIR Spectroscopy . . . . . . . . . . . . . 61.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Overview of methods . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Theory of thin �lm optics 92.1 Single layer of thin �lm . . . . . . . . . . . . . . . . . . . . . . . 92.2 Calculations of re�ectance in a thin �lm of diamond . . . . . . . 11

3 Simulations of re�ectance with Scout software 133.1 Simulation procedure . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 Opto-mechanical modeling with Trace Pro 174.1 TracePro model and method . . . . . . . . . . . . . . . . . . . . 174.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5 Experimental re�ectance measurements 235.1 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 235.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

6 Summarizing discussion 28

7 Conclusions 31

References 32

A Optical constants 33A.1 Optical constants of diamond . . . . . . . . . . . . . . . . . . . . 33A.2 Optical constants of silicon dioxide (SiO2) . . . . . . . . . . . . . 34A.3 Optical constants of silicon dioxide (Si3N4) . . . . . . . . . . . . 36

B Results 37B.1 Theory calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 37B.2 Scout simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 39B.3 TracePro simulations . . . . . . . . . . . . . . . . . . . . . . . . . 45

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1 Introduction

This section intend to give the reader an introduction to properties of diamondand possible applications of diamond thin �lms, to give an understanding of thepurpose for the execution of this master thesis. An overview of di�erent methodsused to investigate thin �lms and the reason for choosing these methods is alsogiven.

1.1 Diamond in bio- and microelectronic applications

In the past decades, new interest in diamond and its possible applications haveemerged. In areas like microelectronics, opto-electronics and biosensor appli-cations the use of diamond has increased dramatically. Previously, diamond'sexcellent electrical, mechanical and optical properties were known but the highproduction cost could not justify the use. In recent time, new production anddeposition techniques to fabricate high-quality diamond with great precisionhave been developed, which make the use of diamond both technically and eco-nomically feasible to be used in a wide range of new technological applications.

In the development of new biosensors, diamond is of great interest. There isa huge demand for new sensor surfaces for sensitive, selective and quantitativebroad spectrum analysis of chemical and biological substances. Analyzing insitu or even in vivo gives many advantages as immediate signal read-out andthe possibility of additional information of molecular interaction and binding,but puts high demand on the sensor surface. The sensor devices must functionin a wide range of environments with shifting pH, temperature, pressure andchemical environment as well as being reproducible and suitable for repeatedusage (mechanical and chemical stable). Most currently used sensor materialsas silicon, glass, polystyrene and possibly also inert metals as gold do not meetthese demands and are therefore not suitable for bioapplications. Diamond,particularly nanocrystalline diamond, however meets most of the above listeddemands as

� High stability and sensitivity in biological environments while also beingcompatible with microelectronic processing technologies.

� Biomolecules such as proteins can be covalently immobilized on a nanocrys-talline diamond surface with simple chemical methods, but still retaintheir biological function. The bond between diamond and a layer ofbiomolecules shows a high stability compared to other often used materialsas gold.

� Bene�cial optical properties as for example high transparency and weakabsorption in a wide frequency range. In nanochristalline diamond (NCD)and ultra-nanochristalline diamond (UNCD) the grain size is in the orderof nanometers. NCD �lms grown on silicon substrates with plasma CVDtechniques can show a optical transparency greater than 84%.1

1Konov V.I. et. al. (1995)

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� Bene�cial electrical and chemical properties.

� Bene�cial mechanical properties as for example extremely high hardness.NCD �lms have a micro-hardness between 75�85 GPa. Surface rough-ness in the order of 5-50 nm for 1 mm thick �lms, signi�cantly decreasesthe transmission in the visible spectrum because of light scattering, buthas negligible e�ect in the IR range. NCD �lms can be fabricated withhigh precision and smoothness that retain diamonds great mechanical andoptical properties and are transparent in the IR region.

Because of its inertness, hardness and optical transparency, diamond is a perfectcoating material in harsh environments.

1.2 Applications in ATR-FTIR Spectroscopy

Attenuated total re�ection Fourier IR spectroscopy (ATR-FTIR) can be usedfor classifying and identi�cation of biomolecules. The basic idea behind thetechnology is the following. Infrared light is passed through the ATR crystal insuch a way that the light is internally re�ected (the so called internal re�ectionelement, IRE). At the interface between the crystal and the medium abovethe crystal, an evanescence �eld is exponentially decaying. The �eld reachestypically just a few micronmeters into the medium. In the IR window mostbiomolecules have typical �ngerprint wavelengths where they absorb light. Bytheir absorption wavelengths it is possible to identify the molecules.

A great advantage with ATR, or any type of so called evanescence wavespectroscopy, is that it can be used to study any molecule, independent ofstate of aggregation, mass size, charge, or �uorescent properties. Diamond isparticularly useful in ATR spectroscopy. Because of its bene�cial mechanicaland thermal (high conductivity) properties as well as inertness diamond makesan excellent IRE material.

Problems arise however when trying to miniaturize IRE diamond biosensorchips, which ideally can be replaced and manipulated with ease. Focusing theIR-beam at the small input area of the IRE-element demands a great aimingcapability and a small beam-surface, two things very di�cult to achieve. Mostlikely a part of the IR beam will miss the input surface and instead hit the abovesurface for example, unless macroscopic diamond IRE slabs are used (such asin commercial diamond ATR accessories. If the diamond IRE-element is athin layer grown on a substrate, interference will develop in the re�ectanceand interfere in the signal. To be able to interpret the signal it is of greatimportance to have a full understanding of the interference caused by diamondand any supporting layers that comprise the IRE. The signal is weak and allinformation about how to receive a better signal is of interest.

1.3 Objectives

The aim of this master thesis was to use di�erent methods to study opticalproperties, mainly re�ectance, in thin �lms of diamond. The primary goal was to

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investigate the possibility of using the advanced ray-tracing software TraceProfor simulation of optical properties in thin �lms using a IR beam focussingassembly and to explore if the basic optical properties can be accounted for withsimpler models. The cause was based on the potential of �nding new informationnot found in simpler models, for the further development of a biosensor basedon the technology described above. As a secondary goal, a comparative studyof the result of the di�erent methods was wanted to get a full picture of theoptical properties of diamond.

Three speci�c cases of diamond �lms on di�erent underlying materials werestudied. The thickness of the diamond �lm varied. This way the dependence ofthickness and underlying material could be explored.

1.4 Overview of methods

The methods used throughout the work are mainly based on already existingtheory and software. By means of three steps described below, a more advancedmodel of a system was created. The most important reason for developing amore sophisticated model was the fact that in reality, the geometry was morecomplicated than the geometry used in simpler models. To get a fully under-standing of the result and to be able to look beyond the limitations of geometryit was of great importance to have a model as similar to reality as possible, thusmaking TracePro a suitable tool.

1. The initial theory of thin �lms (see Section 2) is based on known thin �lmoptics theory derived from Fresnel's equations. Simple cases are possible tocalculate analytically using this theory. Therefore only a case with a singlediamond �lm is calculated analytically using theory of Fresnel's equations.To analyze more complicated cases with multiple �lms, computers andsoftware as those described in step 2 and 3 below are useful.

2. Scout software. The �rst simulations where made using the Scout softwarewhich is based on the theory of Fresnel's equations covered in the theorysection. With the help of Scout it was possible to study multiple lay-ers of thin �lms. This software cannot however simulate more advancedgeometries. It is for example only possible to simulate parallell planarwaves incident on in�nite smooth planes. Simpli�cations compared to thereal experimental situation must be done, especially in regard to angleof incidence and incoupling geometry. Nevertheless the simulations stillgives information of what theory predicts about re�ections in thin �lmsof diamond. And in addition also works as an important comparison toolin the further analysis made in step three. For a detailed description, seeSection 3.

3. TracePro software. The use of TracePro allows better agreement with thereal geometry, including beam focusing and geometry of IRE-microchips.Compared to Scout, Trace Pro uses a totally di�erent method, namely ray-tracing. The software allows building up your own solid models, which

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gives the possibility of building more complicated geometries and lightsources. TracePro is described further in Section 4.

These three methods gave step by step a better understanding of the opticalproperties of the thin diamond �lms. Finally, measurements were made on �lmsamples of the same structure, to test the accuracy of the simulated results.

The following three �lms were studied:

� A single �lm of diamond with thickness 6, 12 and 50 μm.

� Diamond on a 0.5 mm silicon substrate with a 1 μm SiO2 layer. Diamondthickness of 6, 12 and 50 μm was studied.

� Diamond on a 0.5 mm silicon substrate with a 0.2 μm Si3N4 and 1.8 μmSiO2 layer. Diamond thickness of 12 and 30 μm was studied.

By also investigating diamond thin �lms added to a substrate the dependenceof underlying materials could be investigated.

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2 Theory of thin �lm optics

This section outlines the basic thin �lm optics theory which is the basis in allsimulations in the thesis. In cases with multiple �lms, the derivation of thesequantities is much advanced. Especially with an incidence angle di�erent fromnormal incidence. However, the case of a single thin �lm is easier to deriveand the re�ectance is possible to calculate for di�erent angles of incidence. Thefollowing section gives a derivation and calculation of the re�ectance of a singlethin �lm of diamond.

2.1 Single layer of thin �lm

When light is re�ected in a thin �lm, two boundaries have to be taken intoaccount for, which is the upper and lower surface of the �lm. At refractionat a surface of an ordinary object only one boundary is of interest since thethickness can be approximated as in�nite. In a thin layer (see Fig. 1), light willbe re�ected back at the second boundary. When the light is again transmittedthrough the �rst boundary, a phase shift occurs compared to the wave nottransmitted through the �lm. The phase shift is due to the longer distancethe transmitted wave has travelled compared to the re�ected wave. The phaseshift will give rise to interference. As a consequence, the re�ectance gets highlydependent on the �lm thickness and the wavelength of the light.

Fresnel's equations Fresnel's equations are used when studying re�ectionand transmission of light at a boundary and is therefore of obvious use.2 Theequations describe the transmission and re�ection of an electromagnetic waveincident on a plane homogeneous interface:

tp =2N1cosϕ1

N1cosϕ2 +N2cosϕ1(1)

ts =2N1cosϕ1

N1cosϕ1 +N2cosϕ2(2)

rp =N2cosϕ1 −N1cosϕ2

N1cosϕ2 +N2cosϕ1(3)

rs =N1cosϕ1 −N2cosϕ2

N1cosϕ1 +N2cosϕ2(4)

where t is the transmission and r is the re�ection and the lower index p ands specify the polarization state of the wave.

2Ribbing C. G.

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Figure 1: Thin �lm of diamond. n1 = 1 (air), n2 = 2.417 (diamond) andn3 = 3.42 (silicon).

Single layer re�ectance If using the denotation in Fig. 1 the total re�ectionis given from the sum of the individual re�ections. In addition, an extra termδ is added to all terms in the sum to consider the phase shift originated in the�lm. The result is an in�nite sum that can be identi�ed with a geometricalseries, as follows:

r = r1 + t1t′

1r2e−2iδ + t1t

′

1r′

2r′

1e−4iδ + ... = r1 +

t1t′

1r2e−2iδ

1− r2r′1e

−2iδ(5)

To simplify the expression further, Fresnel's equations (see Eq. (1) - (4))give information about the relationship between some of the variables in Eq.(5),

r′

1 = −r1 (6)

andt1t

′

1 = 1− r21 (7)

Insertion of Eq. (6) and (7) into Eq. (5) yields the expression for the re�ection,

r =r1 + r2e

−2iδ

1 + r2r1e−2iδ(8)

The phase change δ originated in the thin �lm can be calculated from thedi�erence in path length covered by the rays. The phase change is given by

δ = −2π

λNz = −2π

λN2d cosϕ2 (9)

where Nz is the optical path di�erence. The phase change will thereforedepend on angle of incidence and wavelength of the light, and refractive indexand thickness of the thin �lm.

With help of Eq. (1)-(4), (8) and (9) it is possible to completely describethe measurable re�ectance, R, of a single layer of thin �lm as follow:

R = rr∗ =r21 + 2r1r2 cos 2δ + r221 + 2r1r2 cos 2δ + r21r

22

(10)

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Figure 2: Re�ectance of a 12 μm diamond �lm in air. Angle of incidence is 80°.

2.2 Calculations of re�ectance in a thin �lm of diamond

As seen above it is possible to calculate the re�ectance if a thin �lm with theuse of Eq. (1)-(4), (9) and (10). The equations are applied on a thin �lm ofdiamond grown on silicon. Fig. 1 describes the situation with a diamond �lmplaced on silicon with in�nite thickness.

Calculations of re�ectance are made on �lms of thickness 12 and 30 μm. Foreach thickness the re�ectance has been calculated for three di�erent angles ofincidence, namely 85º, 80º and 75º. The results for an angle of incidence of 80ºis seen in Fig. 2 and 3. Remaining result is shown in Appendix B.1. The resultshow the wavelength dependence of the re�ectance in the interval 1000 - 5000cm-1for 12 μm and 1000 - 2500 cm-1for 30 μm. Some assumptions are possibleto make to simplify the calculations. The imaginary part of the refractive indexN , that is the coe�cient k, can be neglected, giving a non-absorbing media anda real refractive index n. This is a good approximation except around 2000 cm-1

(see Appendix A.1). Fortunately this region is of less importance spectroscopi-cally since most molecules do not exhibit fundamental vibrations in this region.This assumption will however lead to an overestimation of the re�ectance. Tosimplify the calculations even further, diamond can be assumed to have a almostconstant refractive index in the calculated interval 2-10 μm (see Appendix A.1).Therefore n can be assumed to be independent of λ. The refractive indices usedare air n1 = 1, diamond n2 = 2.376 and silicon n3 = 3.42. Depending on thepolarization Fresnel's equations give di�erent values of re�ection coe�cients. Asa result the re�ectance also depends on the polarization, giving di�erent resultfor p- and s-polarized light. Both re�ectance curves are shown in Fig. 2 and 3,as well as an average value of the two polarization states.

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Figure 3: Re�ectance of a 30 μm diamond �lm in air. Angle of incidence is 80°.

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3 Simulations of re�ectance with Scout software

Scout software is an optical simulation tool for analyzing single or multiplelayers of thin �lms. The software is based on the theory of Fresnel's equationdescribed in Section 2. Scout greatly simpli�es calculations of properties, likefor example re�ectance, of multiple layers of thin �lms.

3.1 Simulation procedure

The procedure for a simulation is as follow:

� In the �rst step the desired materials and material constants are de�ned.Material constants (n, k) for diamond, SiO2 and silicone nitride are im-ported and de�ned in Scout3. Constants for silicon are taken from theScout database for materials. Fig. 4 shows n and k vs. wavenumber inthe IR region for the di�erent materials. From the �gure it can be con-

Figure 4: Values of n and k for diamond, SiO2 and Si3N4.

cluded that diamant has an almost constant refractive index and almostzero absorption.

� In the second step the layer stack is de�ned. This includes choosing thematerials and the corresponding thicknesses. The stack is assumed to bein vacuum.

� In the last step the properties of light and the parameters of the spectrumare de�ned. All the spectra in the result section are shown in interval

3Values of n and k are tabulated in Appendix A

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Figure 5: Re�ectance of a single 12 μm diamond �lm.

1000-5000 cm-1. Simulations are made for both light with p-polarizationand no polarization. The angle of incidence is 75º, 80º and 85º, except forcases with a diamond thickness of 50 μm where only result for an angle ofincidence of 80º is shown.

3.2 Results

The simplest case is that of single diamond layer surrounded by air on bothsides. Optical constants for diamond in Fig. 4 were used in the simulations. Fig.5-6 show results for di�erent diamond �lm thicknesses and polarization. Theangle of incidence is for both simulations 80º. Simulations for di�erent anglesof incidence as well as di�erent diamond thicknesses is shown in Appendix B.2.When only one layer of thin �lm is simulated only one oscillating pattern isshown in the result. A diamond thickness of 12 μm gives a distance of 205 cm-1

between peaks while a thickness of 50 μm gives a distance of 45 cm-1 beetweenpeaks. Eq. (10) and (9) predicts a �lm thickness dependence of the re�ectance.In Fig. 5 and Fig. 6 the distance beetween peaks increases with decreasingthicknesses of diamond �lms as predicted by theory.

Fig. 7 shows results for simulations made on 6 μm diamond added to 1μm silicon dioxide on an silicon substrate. Optical constants from Fig. 4 wereemployed. Simulations were made with light with no polarization as well asp-polarization. The angle of incidence was 80º. Simulations for di�erent anglesof incidence as well as di�erent diamond thicknesses is shown in Appendix B.2.In Fig. 7 the dependence of polarization is clearly shown. Fig. 7 shows howthe re�ectance for light with no polarization is a sum of the re�ectance for lightwith p-polarization and re�ectance for light with s-polarization. The di�erentpolarization states are phase shifted to each other and the obtained expressionsof relectances are di�erent (see Eq. (10)). The result of the phaseshift is the�double-peak� pattern shown in Fig. 7. The added layer of SiO2 gives an extra

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Figure 6: A single 50 μm diamond �lm. Angle of incidence is 80º.

Figure 7: Re�ectance of a 6 μm diamond �lm on 1 μm SiO2 / Si.

interference pattern. In Fig. 7 the peak re�ectances varies in a wave-like motionthroughout the interval of 1 000-8 000 cm-1. This can be compared to Fig. 5-6where only one thin �lm is present and the peak re�ectances are constant. Thedistance between peaks is 372 cm-1.

Fig. 8-9 show results for simulations made on a 12 μm diamond �lm on 0.2μm Si3N4 / 1.8 μm SiO2 / Si. Optical constants from Fig. 4 were employed.Simulations where made with light with no polarization (see Fig. 8) as wellas p-polararization (see Fig. 9). The results in this section show simulationsmade for di�erent angle of incidence and polarization. Simulations with di�erentdiamond thicknesses are shown in Appendix B.2. Fig. 9 clearly show the angledependence of the re�ection. As seen from Eq. (10) the re�ectance depends onthe angle of incidence. The amplitude of the re�ectence increase with a higherangle of incidence. When an extra layer of Si3N4 is added to the layer stack theinterference pattern gets more complicated. The Si3N4layer causes interferencewhich is shown in Fig. 8-9 by the overlaid oscillation in peak re�ectances.The peak separation deduced from this overlaid oscillation agrees well with the

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Figure 8: Re�ectance of a 12 μm diamond �lm on 0.2 μm Si3N4 / 1.8 μm SiO2

/ Si. No polarization.

estimated thickness of the Si3N4 layer.The distance between peaks is 182 cm-1.

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Figure 9: Re�ectance of a 12 μm diamond �lm on 0.2 μm Si3N4 / 1.8 μm SiO2

/ Si. p-polarization.

4 Opto-mechanical modeling with Trace Pro

The result in the previous section is based on Fresnel's equations for multi layerthin �lms and is the accepted approach to treat smooth, thin multilayer �lms. Inthis section these results are tested against Trace Pro simulations. Trace Pro isa software developed by Lambda research group4 and is used mainly for opticalanalysis of solid models. The software is a ray tracing program where individualrays are emitted into a model. Approaching an interface, each ray is analyzedwith respect to possible events like re�ection, refraction, absorption, scatter anddi�raction. All through the ray path, the software keeps track of changes in �uxand direction of each ray. In the software-environment it is possible to createsolid models to imitate existing models. Each model and surface can be de�nedproperties like material, coatings, color etc. It is also possible to de�ne stacksof thin �lms, which was used often throughout the work.

The following section describes the model created in Trace Pro and thede�ned properties of the model. For a description of the experimental setupused in the measurements and also used as a model for the model built inTrace Pro, the reader is referred to Section 5. Brie�y, the Trace Pro model isconstructed to mimic the Cassegrain type infrared focusing assembly used in theexperiments. Covered in this chapter as well, is the result from the simulation.

4.1 TracePro model and method

The aim when building up the model in TracePro was to come as close as possibleto the experimental conditions described in the next section.. The template wasthe mirror system in the spectrometer used to do the measurements of existing

4For more information about TracePro see http://www.lambdares.com/

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Figure 10: Model used in TracePro. A: Perfect re�ector, focusing light emittedfrom plane C. B: Polarizer, active when p-polarized light is simulated. C:Ray source, emits rays perpendicular to surface in the negative z-direction.D:Absorber, removes beams corresponding to a hole in the centre of re�ectorA. E: Substrate with applied thin �lm properties. F: Detector mirror.

�lms. Simpli�cations in the structure of the mirror system were possible to makewithout losses in information. The model was gradually adjusted to accomodatecertain aspects of the experimental set up and model system. Fig. 10 show thesix parts built to the model. The acronyms in the text below refer to the lettersin the �gure.

Substrate (E) The substrate corresponds to a block with dimensions 10 x 10x 0.5 mm with centre position at (0,0,0.25) according to the coordinate systemin Fig. 10. A thin �lm stack was applied to the surface in the positive y-direction. Materials and the corresponding thicknesses were de�ned dependingon which case was simulated. Material constants for diamond, SiO2 and Si3N4

were imported to TracePro and were the same used in Scout (see AppendixA). Material constants used for silicon was prede�ned in TracePro materialdatabase. To avoid rays coming from beneath or the side of the substrate to bere�ected and hit the detector mirror and interfere with the result, all surfacesexcept the surface with a normal componant in the y-direction (see Fig. 10)were applied properties of perfect absorbers. As a consequence, rays hittingthe absorber surfaces is fully absorbed and the ray tracing of these rays isterminated.

Ray source (C) A plane was chosen as a surface source. The rays wereevenly distributed throughout the surface and emitted normal to surface. The

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emission type was black body radiation with a temperature at 700 K. Accordingto Wien's displacement law the temperature gives a emission intensity maximumat a wavelength approximatly 3.3 μm. This is in reasonable agreement with theemission in the infrared spectrometer employe din the experiments, where a SiC(so called Globar) light source was used. When the interval 1000-5000 cm-1

was simulated the total number of emitted rays was chosen to be 300 000. Butthis number works only as a goal for TracePro. TracePro distribute the raysfor each wavelength so the total emission curve looks like black body radiation.The total number of rays were then 413 088. In TracePro the user chooses thenumber of discrete wavelengths wanted in an interval. When simulating theinterval 2 � 10 μm, most wavelengths wished to be in the interval to get thebest data in the that interval. Between 2 and 3 μm the number of wavelengthswere set to 170 and between 3 and 10 μm the number of wavelengths wereset to 240. The �ux for each ray depends on the number of rays with thesame wavelength, as the total �ux distribution must correspond to a black bodyradiation. TracePro calculates the �ux for each ray. The minimum number ofrays for each wavelength was set to 700. This means that each wavelength hasa minimum 700 rays but wavelengths with higher intensity have more rays thanthe minimum limit.

When a detailed simulation in the interval 5-6.67 μm (1500-2000 cm-1) wasmade, it was necessary to add more wavelengths to this interval. The followingparameters were used: minimum rays = 1000, total rays = 300 000, number ofwavelengths in interval 5-6.67 μm = 200. In the remaining intervals, which areabove and beneath the interval of interest, one wavelength each was added.

Re�ecting mirror (A) The re�ecting mirror was used to focus the rays ona single spot on the substrate. The geometry of the focused light in TraceProwas chosen to mimic the geometry of the infrared focusing assembly in the spec-trometer used in the measurements. Fig. 14 in Section 5.2 gives the parametersof the spectrometer mirror. Instead of building an exact copy of the Cassegrainmirror system only a single re�ecting mirror was used. This yielded however thesame geometrical properties of the focused light incident on the sample surfaceas the spectrometer mirrors. Besides wavelength and �ux, the parameter ofinterest was the cone angle of the re�ected light which was 23.6º. The followingparameters were applied to re�ecting mirror A to give the correct cone angle:Parabolic shape, focal length =59.8659 mm, length=2.61 mm, diameter=50mm, thickness=1·10-5 mm. The mirror was placed at position (0,0,-59.8659)according to the coordinate system in Fig. 10. The surface was made a perfectre�ector. As the area of the mirror is less than the area of surface source C,some of the rays will pass the mirror without being re�ected.

Detecting mirror (F) The detecting mirror was applied the same geometri-cal properties as re�ecting mirror A. The position was changed to (0,0,59.8659)and rotated 180º about the x-axis. The surface was made a perfect absorber.

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Polarizer (B) The polarizer object was only active when light with polariza-tion was simulated. Rays emitted from surface source C have no polarization.When the rays pass the polarizer the rays change polarization according to thesettings of the polarizer surface. To simulate light with p-polarization the polar-izer was chosen to be linear with a vertical transmission axis in the (x,z)-plane.TracePro calculated the Mueller matrix of the polarizer. Only rays emitted fromthe surface source (that is in the negative z-direction) should be subjected topolarization. Therefore the propagation direction was set to (0,0,-1) and the�up� direction to (0,1,0). With �up� direction means the up direction of thepolarizer object.

Absorber (D) The purpose of the cylindrical object D is to absorb raysre�ected from the centre of the re�ector mirror A. This function is meant tosimulatel the e�ect of the two-mirror system of the Cassegrain mirror in thespectrometer where only an annulus are transmitted through the lens (see Fig.14 in Section 5.2). Rays with a smaller cone angle than 9.8º are not focused ontothe substrate. To absorb the correct angles the following geometrical parameterswas applied to the cylinder: radius=3.45 mm, length=1 mm. The cylinder waspositioned at (0,0,-20) according to the coordinate system in Fig. 10.

Method The simulation was made using trace ray. Some changes to thedefault settings were made but most settings were selected as default values.The �ux threshold was set to 1e-15. When the �ux carried by a ray is below thethreshold, the ray tracing of the ray is terminated. Because each ray carriedinformation and was important for the total result, no termination of ray tracingwas desired. The �ux threshold was therefore set to a low value. Changing the�ux threshold is also important for the data processing. Confusion can arise ifthe number of rays re�ecting the substrate is less the number of rays incidentthe surface.

The �ux of each ray incident on a surface is displayed in incident ray table.Both the �ux of the rays hitting the substrate and rays hitting the detector sur-face can be displayed in tables. With values from these two tables it was possibleto calculate a re�ectance value for each ray. An average value of the re�ectancefor each wavelength was calculated to obtain the wavelength-dependence of there�ectance. The result of the simulations and calculations are presented in thenext section.

4.2 Results

Fig. 11-13 show results from TracePro simulations made with the above de-scribed conditions. In Appendix B.3 the remaining results for di�erent diamondthicknesses and substrates not shown in this section are presented. In Fig. 11re�ectance of a single 12 μm diamond layer have been investigated. Both lightwith no polarization and p-polarization have been used. The re�ectance haveone interference pattern caused by the single thin �lm. Peak re�ectance for

20

Figure 11: Re�ectance of a single 12 μm diamond �lm.

p-polarized light (~0.4) is lower than peak re�ectance for light with no polariza-tion (~0.7) as expected from previous simulations and calculations (see Fig. 5).The re�ectance values obtained with TracePro in Fig. 11 are in close proximityto equal to the re�ectance values seen in Scout simulation (see Fig. 5). Thedistance between peaks is approximatly 199 cm-1.

Fig. 12 shows results for 6 μm diamond on 1 μm SiO2, added to a siliconsubstrate. The re�ectance for light with with no polarization show a �double-peak� pattern caused by the combination of the two polarization states. Thedistance between peaks are approximatly 372 cm-1. At approximatly 1200 cm-1

there is a re�ectance maximum similar to the corresponding maximum seen inFig. 7, but the TracePro simulation seen here gives a higher maximum value.

Fig. 13 shows result for 12 μm diamond on 0.2 μm Si3N4 and 1.8 μm SiO2,added to a silicon substrate. Here too there is a �double-peak� pattern caused bythe phase shift of the two polarization states. The added Si3N4layer also resultin extra interference seen as variations in peak re�ectances. These variationswas also seen in Scout simulations in Fig. 8-9. Because of fewer data pointsaround 2 000 - 3 000 cm-1and smaller variations between re�ectance values it isdi�cult to interprent the result in this region for simulation made on light withno polarization. The distance between peaks are approximatly 182 cm-1.

21

Figure 12: Re�ectance of a 6 μm diamond �lm on 1 μm SiO2 / Si.

Figure 13: Re�ectance of a 12 μm diamond �lm on 0.2 μm Si3N4 / 1.8 μm SiO2

/ Si.

22

5 Experimental re�ectance measurements

5.1 Samples

Measurements were made on four di�erent samples, all with di�erent diamondthickness and underlying coating material. Diamond �lms from di�erent batchesprepared by slightly di�erent methods as well as a free standing single crystalslab were employed.

� 50 μm thick, single crystal free standing diamond slab (5 x 5 mm width).

� 6 μm thick polycrystalline diamond grown on a silicon substrate coatedwith a 1 μm thick SiO2 layer. The diamond �lm was deposited usinga hot-�lament CVD technique. The diamond �lm only covered an areaof about 2x2 mm. This sample was known to exhibit the lowest opticalquality of the tested samples.

� 12 μm thick polycrystalline CVD diamond on a silicon substrate coatedwith 0.2 μm Si3N4 and 1.8 μm SiO2. The polycrystalline diamond wasgrown by CVD in microwave plasma.

� 16 μm thick polycrystalline CVD diamond grown on a silicon substratecoated with 0.2 μm Si3N4 and 1.8 μm SiO2. The polycrystalline diamondwas grown by CVD in microwave plasma. A square well was etched in thesilicon substrate, yielding a free standing 16 μm polycrystalline diamondmembrane structure.

5.2 Experimental setup

Infrared re�ectance measurements were performed on a Fourier transform in-frared (FTIR) spectrometer (Bruker IFS 66v/S), which allowed measurementsto be performed either in air or vacuum after evacuation of the sample com-partment. The focusing mirror system was a type of Cassegrain mirror. Thedimensions of the mirror system are shown in Fig. 14. There were four degreesof freedom when adjusting the position of the sample holder and the mirrors.First the mirror used for focusing the beam on the sample could be adjustedalong the beam axis to align the focal point onto the sample. Second the collect-ing Cassegrain objective could be adjusted to compensate for the adjustmentof focal point. Both mirrors were placed at a distance of ca. 24 mm from thesample in order for the beam to hit the centre of the �lm sample. Finally thesample holder was vertically adjustable and laterally adjustable perpendicularto the incoming light.

Two types of measurements where made on each �lm sample, �rst in air andsecondly in vacuum. The �rst measurement where made in two steps. First thelight intensity where measured without the beam hitting the �lm. The resultwas a black body radiation spectrum. The black body spectrum was used asa background (the so called single channel background spectrum). The sampleholder was then moved so the light hit the �lm and an interference pattern

23

Figure 14: Cassegrain mirror. Dimensions are A=49 mm, B=9.72 mm, C=38.6mm, D=23.7 mm, E=9.8°, F=23.6°.

was observed. The re�ectance was calculated by dividing the sample singlechannel spectrum with the background single channel spectrum. By doing sothe in�uence of absorption by gas molecules could partly be accounted for.

The second measurement was made in vacuum. In this way "cleaner" spec-tra, not in�uenced by gas absorption, could be obtained. Measurements weremade in the wavelength region 600 � 8000 cm-1. The number of data pointswere 3838, giving a spectral resolution of approximately 1.9 cm-1 between eachdata point. Measurements of a single 50 μm diamond �lm were only made inair because of di�culty to position the fragile single crystal slab in the sampleholder.

Result of measurements made in air will be presented as transmittance ver-sus wavenumber. But the measured values of transmittance do not give anyinformation about the real absolute values of transmittance. This because howthe background single channel spectra has been de�ned. The background in-tensity is the intensity of the total beam emitted by the spectrometer and hitthe collecting Cassegrain objective with almost full intensity. When the next�lm measurement is made, all light will not hit the �lm. This because the lightincident upon the �lm edge formed as a cone, making only the upper half ofthe beam hit the �lm surface. But the background intensity corresponds to thefull light cone. Therefore it is not possible to make any conclusions about theabsolute values of transmittance from the result. It is, however, not the aim ofthe measurements to �nd out exact values of transmittance, but rather to look

24

at the interference pattern.

5.3 Results

The results from the measurements are shown in Fig. 15-17. Fig. 15 show theresult of measurements made on a single 50 μm diamond �lm. The measurementwas made only in air. The distance between peaks is approximately 46 cm-1.

Figure 15: Measured transmission in a single 50 μm diamond �lm.

Fig. 16 shows the results from measurements made on a single 12 μm di-amond �lm. The measurement made in vacuum shows a blockbody spectrumwith interference caused by the thin �lm of diamond. The distance betweenpeaks is approximately 165 cm-1.

Fig. 17 shows the result of the measurements made on a 6 μm diamond �lmon 1 μm SiO2, added to a Si-substrate. In both measurements signs of a �double-peak� structure are shown. In the measurement made in air the interferencepattern is not as clearly shown as in the measurement made in vacuum. Thedistance between peaks is approximately 282 cm-1.

Fig. 18 shows the result from measurements made on a 12 μm diamond �lmon 0.2 μm Si3N4/ 1.8 μm SiO2/Si. In the region 1 500 - 2 000 cm-1there aredetectable signs of �double-peak� structure, expected from previous sections forlight with no polarization. Around 2 500 cm-1and 4 750 cm-1 there are lesservariations in re�ectance compared to remaining regions. This is part of a largervariation caused by interference from the Si3N4 layer. The distance betweenpeaks remains the same throughout the interval and is approximately 166 cm-1.

25

Figure 16: Measured transmission in a single 12 μm diamond �lm. The mea-surements are made in a) air, b) vacuum.

Figure 17: Measured transmission in a 6 μm diamond �lm on a SiO2/ Si. Themeasurements are made in a) air, b) vacuum.

26

Figure 18: Measured transmission in a 12 μm diamond �lm on a Si3N4/ SiO2/Si. The measurements are made in a) air, b) vacuum.

27

6 Summarizing discussion

In previous sections results obtained through di�erent methods have been shown.First Scout was used to obtain a result based on Fresnel's equations for multi-layer thin �lms, which is the accepted theory to treat smooth thin �lms. Sec-ondly, simulations were made with TracePro and in the last step, experimentalmeasurements provided result to test the simulated result against. The resultfrom these three methods will be compared to each other.

The Scout results are consistent with the developed theory in section 2.For each thin layer an extra interference pattern is shown in the re�ectance.Eq. (10) gives the correlation between re�ectance, layer thickness and angle ofincidence and the thickness dependence is contained in the phase shift δ. In Fig.19a δ is plotted versus �lm thickness d and shows how the phase shift increaseslinearly with �lm thickness. This is consistent with the obtained result wherethe interference increases with thickness.

(a) (b)

Figure 19: a ) Phaseshift versus �lm thickness. δ = − 2πλ N2d cos(ϕ2) according

to Eq. (9). b) The polarization dependence of interference.

In Scout simulations in Fig. 7-9 the dependence of polarization which con-�rms how polarization a�ects re�ectance through di�erent expression for theFresnel's equation (see Eq. (1)-(4)) is seen. Fig. 19b illustrates the depen-dence of polarization by showing one term of the equation for re�ectance (seeEq. (10)), which contains Fresnels equation r1 and r2. r1 and r2 is di�erent fors-polarization and p-polarization which leads to a changing interference pattern.

When comparing results from Scout with simulations made with TracePro,the result is consistent. The result show dependence of thickness and polariza-tion as expected from Eq. (10) and Scout result. Statistical methods are usedin TracePro as well as in the data processing methods to obtain the result. Thisexplains the indistinct result in the region 2 400 - 3 250 cm-1 as the data wasnot enough to produce smooth curves. There is therefore di�cult to obtain in-formation about maximum and mimium values in cases with diamond added toa substrate, because of a more complex interference pattern. In Fig. 11, whichshow a single layer of 12 μm diamond, the re�ectance is approximatly 0.4 forp-polarization and 0.7 for no polarization. The same values are obtained whenthe same case is studied with Scout with 80º angle of incidence (see Fig. 11).It can be concluded that the e�ective angle of incidence can be approximated

28

Scout TracePro Meas.

12 μm diamond 205 199 -16 μm diamond - - 16550 μm diamond 45 45 46

6 μm diamond / SiO2/ Si 372 372 28212 μm diamond / Si3N4/ SiO2/ Si. 182 182 166

Table 1: Distances between peaks obtained with Scout, TracePro and measure-ments. Values in units of cm-1.

to 80º in the model in TracePro.The distance between peaks can be used as a tool to compare interference

pattern obtained by each method. Table 1 shows a summary of measured peakdistances of the obtained result for Scout, TracePro and measurements. Themeasurement of a single 50 μm diamond �lm shows the most similar valueto the measurements compared to simulations. The sample had the highestquality and the best determined thickness. Remaining samples were more likelyto di�er in thickness because of the used growth process. Scout and TraceProgive similar values of peak distance in all four cases, which imply that TraceProwell simulates interference of thin �lms.

The results from the measurements show some di�erences compared to resultobtained with Scout and TracePro. Since light with no polarization was used inthe measurements, the re�ectance is expected to show the same �double-peak�structure caused by overlapping of light with di�erent polarization states as seenin the simulations. In contrary to expectations, the measured results of diamondgrown on SiO2/Si and Si3N4/SiO2/Si are similar to results obtained previouslyfor p-polarized light, except for the region 1 300-2 000 cm-1 in Fig. 17 and Fig.18 where small tendencies of overlapping are seen. The �double-peak� structureis seen most clearly when no layer of Si3N4 has been added. Several reasonscan be discussed to explain this behaviour. To begin with, the amplitude of there�ectance di�ers for di�erent polarizations. Fig. 20 shows the theoretical ratioRs/Rp versus wavelength to demonstrate how s-polarized light dominates there�ectance. The opposite apply to the transmittance, leading to a dominationof p-polarized light. Fig. 20 shows how the re�ectance can be up to 15 timeshigher for p-polarized light than s-polarized light.

Measurements show that when a layer of SiO2 or Si3N4 is present, less ofthe s-polarized light is transmitted and seen in the result than expected fromsimulations and theory. In the region 1 000-1 200 cm-1 SiO2 absorbs lightbecause of lattice vibrations which e�ects the light transmitted through the�lm and hence should e�ect the measurements. It can be assumed that Si3N4

also a�ects the properties of passing light. If comparing the measurement ofdiamond grown only on SiO2/Si with the measurement of diamond grown on

29

Figure 20: Ratio between Rs/Rp versus wavelength for 12 my diamond onsilicon. Angle of incidence is 80 degrees. Eq. (10) gives the expressions for Rs

and Rp.

SiO2 / Si3N4/Si there is less �double-peak� structure when Si3N4 has beenused. Therefore Si3N4 is a probable cause for the domination of p-polarizedlight. �Double-peak� structure is less shown at shorter wavelengths (> 2 000cm-1) which imply that as the wavelength approaches the layer thickness (0.8μm) less s-polarized light is shown in the measurements suggesting a thicknessdependence.

30

7 Conclusions

Layer thickness, angle of incidence and polarization have all a great in�uenceon interference. Interference increases with thickness and is sensitive to smallvariations in thickness. It is therefore important to be able to grow diamond�lms with well determined thickness to have full control over the behaviour oflight travelling in the �lm. Angle of incidence e�ects the amplitude of re�ectanceand from TracePro simulation it can be concluded that the angle of incidenceof the model can be approximated as 80º.

Simulations with TracePro give consistent results with both theory and Scoutresults. It is concluded that the simple parallel beam geometry used in Scoutwith 2D �lm geometries is su�cient to model the basic physical properties ofthe microfabricated diamond chip structures investigated here. While no extrainformation is obtained using TracePro compared to Scout it is valuable formore advanced geometries. More data as well as better techniques for dataprocessing would however improve the accuracy of the result.

In spectrometry applications it is vital to have a high signal for analysis,which makes it important to minimize the e�ect of the coating material to theintensity of the out-put signal. A deeper investigation of the e�ect of coatingmaterial on di�erent polarizations might explain why p-polarization dominatesthe result in measurements more than in simulations. Measurements using lightwith polarization would be necessary to get a better insight into the dependenceof polarization and the dependence of layer thickness of especially Si3N4. Mini-mizing the thickness of the coating material might give a higher signal when nopolarization is used as a light source. Most favourable would be to use polarizedlight.

31

References

[1] P.O. et al. Andersson. A novel atr-ftir approch for characterisation andidenti�cation of ex situ immobilisation species. ChemPhysChem, vol. 8:p.712�722, 2006.

[2] E. Hecht. Optics. Addison-Weasley, 4 edition, 2002.

[3] A. et al. Härtl. Protein-modi�ed nanocrystalline diamond thin �lms forbiosensor applications. Nature Materials, vol 3:p. 736�742, 2004.

[4] M. Karlsson and F. Nikolaje�. Diamond micro-optics: microlenses and an-tire�ection structured surfaces for the infrared spectral region. Optics ex-press, 11(5):p. 502�507, 2003.

[5] V.I. et. al. Konov. Nanocrystalline diamond �lms: new material for ir optics.Proc. SPIE, 2428:p. 612�620, 1995.

[6] C.G. Ribbing. Introduction to material optics. Collected notes.

[7] W. et al. Yang. Dna-modi�ed nanocrystalline diamond thin �lms as stable,biologically active substrates. Nature Materials, vol. 1:253�257, 2003.

[8] A.M. Zaitsev. Optical properties of diamond, A data handbook. Springer,2001.

32

A Optical constants

A.1 Optical constants of diamond5

Wavelength n Absorption coe�cient knm cm-1 10-7

2000 2.383 0.05 7.957752500 2.382 0.05 9.947183000 2.382 2 477.4654000 2.376 5 1591.555000 2.376 10 3978.87

5500 2.376 1.1 481.4446000 2.376 1 477.4657000 2.376 0.2 111.4088000 2.376 0.12 76.39449000 2.376 0.1 71.6197

10000 2.376 0.07 55.704211000 2.376 0.07 61.274712000 2.376 0.07 66.8451

5Zaitsev (2001)

33

A.2 Optical constants of silicon dioxide (SiO2)

Wavelength n knm

2000 1.441747573 02500 1.441747573 0

2566.60746 1.441747573 02636.861314 1.441747573 02711.069418 1.427184466 0

2789.57529 1.427184466 02872.763419 1.427184466 02961.065574 1.427184466 03054.968288 1.412621359 03155.021834 1.412621359 0

3261.851016 1.412621359 03376.168224 1.398058252 03498.789346 1.398058252 03630.653266 1.398058252 03772.845953 1.398058252 0

3926.630435 1.398058252 04093.484419 1.398058252 04275.147929 1.383495146 04473.684211 1.383495146 04691.558442 1.368932039 0

4931.740614 1.368932039 05197.841727 1.354368932 05494.296578 1.325242718 05826.612903 1.296116505 06201.716738 1.252427184 0

6628.440367 1.194174757 07118.226601 1.077669903 07686.170213 0.757281553 0.0582524278005.540166 0.451456311 0.5097087388352.601156 0.524271845 0.873786408

34

8731.117825 0.451456311 2.5048543699145.56962 2.169902913 1.864077679601.328904 2.985436893 0.87378640810104.8951 2.257281553 0.08737864110664.20664 1.82038835 0.02912621411289.0625 1.660194175 0.02912621411991.70124 1.849514563 0.262135922

35

A.3 Optical constants of silicon dioxide (Si3N4)

Wavelength n knm

2000 2.013333333 02500 2.013333333 0

2582.056893 2.013333333 02669.683258 2.013333333 02763.466042 2.013333333 0

2864.07767 2.013333333 02972.292191 2.013333333 0.0173089.005236 2.013333333 03215.258856 2.013333333 03352.272727 2.013333333 0

3501.48368 2.013333333 03664.596273 2.013333333 03843.648208 2 04041.09589 1.986666667 04259.927798 1.973333333 0

4503.816794 1.96 0.034777.327935 1.986666667 05086.206897 1.96 05437.788018 1.933333333 05841.584158 1.92 0

6310.160428 1.893333333 06860.465116 1.826666667 07173.25228 1.8 07515.923567 1.746666667 07892.976589 1.68 0.026

8309.859155 1.613333333 0.088773.234201 1.493333333 0.1159291.338583 1.146666667 0.4699874.476987 1.066666667 0.88510535.71429 1.266666667 1.327

11291.86603 1.853333333 1.5412164.94845 2.6 1.575

36

B Results

B.1 Theory calculations

Figure 21: Re�ectance of a 12 μm diamond �lm surrounded by air. Angle ofincidence is 75°.

Figure 22: Re�ectance of a 30 μm diamond �lm in air. Angle of incidence is75°.

37

Figure 23: Re�ectance of a 12 μm diamond �lm in air. Angle of incidence is 85°

Figure 24: Re�ectance of a 30 μm diamond �lm in air. Angle of incidence is 85°

38

B.2 Scout simulations

Figure 25: A single 12 μm diamond �lm. No polarization.

Figure 26: A single 12 μm diamond �lm, p-polarization.

39

Figure 27: A single 6 μm diamond �lm. No polarization.

Figure 28: A single 6 μm diamond �lm, p-polarization.

40

Figure 29: A 6 μm diamond �lm on 1 μm SiO2 / Si. No polarization.

Figure 30: A 6 μm diamond �lm on 1 μm SiO2 / Si. P-polarization.

41

Figure 31: A 12 μm diamond �lm on 1 μm SiO2 / Si. No polarization.

Figure 32: A 12 μm diamond �lm on 1 μm SiO2 / Si. P-polarization.

42

Figure 33: A 50 μm diamond �lm on 1 μm SiO2 / Si. Angle of incidence is 80º.

Figure 34: Re�ectance of a 30 μm diamond �lm on 0.2 μm Si3N4 / 1.8 μm SiO2

/ Si. No polarization.

43

Figure 35: Re�ectance of a 30 μm diamond �lm on 0.2 μm Si3N4 / 1.8 μm SiO2

/ Si, p-polarization.

44

B.3 TracePro simulations

Figure 36: Re�ectance of a diamond �lm on a SiO2/ Si3N4/ Si-substrate. Nopolarization. a) Diamond thickness 12 μm. b) Diamond thickness 30 μm. c)Diamond thickness 30 μm, in interval 1500-2000 cm-1.

45

Figure 37: Re�ectance of a diamond �lm on a SiO2/ Si-substrate. No polariza-tion. a) Diamond thickness 6 μm. b) Diamond thickness 12 μm.

Figure 38: Re�ectance of 50 μm diamond on a SiO2/ Si-substrate. No polariza-tion.

46

Figure 39: Re�ectance of a single diamond �lm. No polarization. a) Diamondthickness 6 μm. b) Diamond thickness 12 μm.

Figure 40: Re�ectance of a single 50 μm diamond �lm. No polarization.

47

Figure 41: Re�ectance of light with p-polarization in a single �lm of diamond.a) Diamond thickness 6 μm. b) Diamond thickness 12 μm.

Figure 42: Re�ectance of light with p-polarization in a single 50 μm �lm ofdiamond.

48

Figure 43: Re�ectance of light with p-polarization in diamond covering a SiO2/Si-substrate. a) Diamond thickness 6 μm. b) Diamond thickness 12 μm.

Figure 44: Re�ectance of light with p-polarization in 50 μm diamond on a SiO2/Si-substrate.

49

Figure 45: Re�ectance of light with p-polarization in diamond covering a SiO2/Si3N4/ Si-substrate. a) Diamond thickness 12 μm. b,c) Diamond thickness 30μm.

50